### Starbucks' 2019 Annual Property Size Report The following data provides an overview of Starbucks' property sizes, which facilitate roasting, manufacturing, warehousing, distribution, and corporate administrative operations. The information pertains to seven specific locations: | Location | Approximate Size in Square Feet | Purpose | |--------------------|--------------------------------|----------------------------------------------| | Minden, NV (Carson Valley) | 1,080,000 | Roasting, warehousing, and distribution | | York, PA | 1,957,435 | Roasting, warehousing, and distribution | | Lebanon, TN | 680,000 | Warehousing and distribution | | Auburn, WA | 491,000 | Warehousing and distribution | | Kent, WA | 510,000 | Roasting and distribution | | Seattle, WA | 1,283,000 | Corporate administrative | | Shanghai, China | 177,000 | Corporate administrative | #### Questions for Analysis 1. What is the average size of properties across these 7 locations? 2. Assuming the property sizes follow a Normal distribution with a mean of 980,000 square feet and a standard deviation (SD) of 310,000 square feet: - a. What is the z-score of the York property size? - b. What percentage of properties are larger than the Auburn property? - c. Which properties have a z-score equal to or larger than 1? - d. Which properties' sizes reach the top 10%?

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Starbuck’s 2019 Annual Report shows that the Approximate sizes in Square Feet of the properties for 7 locations are:

What is the average size of properties across these 7 locations?

If the size of the properties follows a Normal distribution with a mean of 980,000 sqft and SD of 310,000 sqft,
1. What is the z score of York property size?

What percentages of properties larger than Auburn property?

Which properties have a z score equal or larger than 1?

Which properties’ size reach the top 10%?

### Starbucks' 2019 Annual Property Size Report

The following data provides an overview of Starbucks' property sizes, which facilitate roasting, manufacturing, warehousing, distribution, and corporate administrative operations. The information pertains to seven specific locations:

| Location | Approximate Size in Square Feet | Purpose |
|--------------------|--------------------------------|----------------------------------------------|
| Minden, NV (Carson Valley) | 1,080,000 | Roasting, warehousing, and distribution |
| York, PA | 1,957,435 | Roasting, warehousing, and distribution |
| Lebanon, TN | 680,000 | Warehousing and distribution |
| Auburn, WA | 491,000 | Warehousing and distribution |
| Kent, WA | 510,000 | Roasting and distribution |
| Seattle, WA | 1,283,000 | Corporate administrative |
| Shanghai, China | 177,000 | Corporate administrative |

#### Questions for Analysis

1. **What is the average size of properties across these 7 locations?**

2. **Assuming the property sizes follow a Normal distribution with a mean of 980,000 square feet and a standard deviation (SD) of 310,000 square feet:**
- a. What is the z-score of the York property size?
- b. What percentage of properties are larger than the Auburn property?
- c. Which properties have a z-score equal to or larger than 1?
- d. Which properties' sizes reach the top 10%?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Expert Solution

Step 1

1.) Here, we have observations on 7 locations, x1,x2,...,x7. Then, the average size of 7 location is

$x = \frac{x 1 + x 2 + x 3 + x 4 + x 5 + x 6 + x 7}{7} = \frac{6178435}{7} = 882633.5714 s q f t$

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